Question: A circle has a radius of $2$. An arc in this circle has a central angle of $225^\circ$. What is the length of the arc? {4\pi} {225^\circ} \color{#DF0030}{\dfrac{5}{2}\pi} {2}
Solution: First, calculate the circumference of the circle. $c = 2\pi r = 2\pi (2) = 4\pi$ The ratio between the arc's central angle $\theta$ and $360^\circ$ is equal to the ratio between the arc length $s$ and the circle's circumference $c$ $\dfrac{\theta}{360^\circ} = \dfrac{s}{c}$ $\dfrac{225^\circ}{360^\circ} = \dfrac{s}{4\pi}$ $\dfrac{5}{8} = \dfrac{s}{4\pi}$ $\dfrac{5}{8} \times 4\pi = s$ $\dfrac{5}{2}\pi = s$